# Number System - Natural Numbers (cardinal and ordinal numbers) - <math>\mathbb{N} </math>

> (Data|State) Management and Processing > (Data Type|Data Structure) > Number, Numeric, Quantity > Number System (Classification|Type)

### Table of Contents

## 1 - About

A natural number <math>\mathbb{N} </math> can be used for two purposes:

- to count (ie describe the size of a set)
- to order (ie or to describe the position of an element in a sequence).

0, 1, 2, 3, 4, ... or 1, 2, 3, 4,

The natural numbers are those used for:

Operation | Example | Words |
---|---|---|

counting | there are six coins on the table | cardinal numbers |

ordering | this is the third largest city in the country | ordinal numbers |

## 2 - Articles Related

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## 3 - Number systems

## 4 - Representation

### 4.1 - Symbol

In the base 10 numeral system, the symbols for natural numbers are written using ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

### 4.2 - Class

In set theory, natural numbers can be represented by classes of equivalent sets. For instance, the number 3 can be represented as the class of all sets that have exactly three elements.

## 5 - Documentation / Reference

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